MITC technique extended to variable kinematic multilayered plate elements

Assessment of MITC plate elements based on CUF with respect to distorted meshes

Refined shell elements for the analysis of functionally graded structures

In this work a nine-nodes shell finite element, formulated in the framework of Carrera’s Unified Formulation (CUF), is presented. The exact geometry of cylindrical shells is considered. The Mixed Interpolation of Tensorial Components (MITC) technique is applied to the element in order to overcome shear and membrane locking phenomenon. High-order equivalent single layer theories contained in the CUF are used to perform the analysis of shell structures. Benchmark solutions from the open literature are taken to validate the obtained results. The mixed-interpolated shell finite element shows good properties of convergence and robustness by increasing the number of used elements and the order of expansion of displacements in the thickness direction.

Propagation of Lamb waves in multilayered elastic anisotropic plates is studied in the framework of combination of the six-dimensional Cauchy formalism and the transfer matrix method. The closed form secular equations for dispersion curves of Lamb waves propagating in multilayered plates with arbitrary elastic anisotropy are obtained.

Thermoelasticity of multilayered plates with imperfect interfaces

In this paper, the node-based smoothed finite element method is developed for three-node triangular plate elements using the mixed interpolation of tensorial components (MITC) technique to remove the shear locking. The C 0-type continuous plate elements represent the higher-order shear deformation theory of laminated composite plates by adding two degree of freedoms related to derivatives of deflection. Based on the MITC3 technique for three-node triangular degenerated shell elements, an explicit formulation of gradients of the transverse shear strains is derived. The constant strain fields within the C 0-type continuous plate elements are averaged over node-based domains defined by connecting the centroids and edges’ middle points of elements having common nodes. The proposed elements, namely NS-MITC3, show good accuracy and convergence as compared to other plate elements when employed to analyze laminated composite plates.

The development of a triangular multilayer sandwich plate element with n stiff layer and n-l weak cores is presented. The element is applied to several standard bending and vibration problems and good accuracy is demonstrated. The complex problem of the free vibration of a five-layer swept-back cantilever plate is included to show the versatility of the method.

This article deals with layer-wise (LW) models for composite and sandwich plates. Refined layer-wise models are built according to the Carrera Unified Formulation (CUF), which has been developed over the last decade for beams, plate, and shell theories. CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. In this article, displacement variables are expanded along the layer thickness through Legendre polynomials. Comparisons with previous analysis based on equivalent single layer (ESL) approaches are given. The effect of each term of the expansion on the accuracy of stress/displacement components for the static response of composite and sandwich plates is analyzed. Ineffective terms are discarded from the expansion in order to save computational cost. The reduced models obtained, which are denoted as mixed axiomatic/asymptotic models, are as accurate as full expansion models. Numerical analysis is restricted to closed-form solutions via Navier-type solutions. A number of problems related to laminated and sandwich structures are solved and related reduced models are built by varying geometrical, lay-up, and mechanical parameters. Results show that in some cases (in particular those related to sandwich plates) reduced layer-wise models can save up to 50% of the degrees-of-freedom of the full models without significant accuracy losses. It is found that the significant terms related to reduced models are very much subordinated to the problems considered and that from that point of view the use of a framework that can generate any theory, such as CUF, appears very suitable to build reduced models for plates.

A four-node MITC finite element for magneto-electro-elastic multilayered plates

In this paper, free vibration finite element analysis of axially moving laminated composite beams subjected to axial tension is studied. It is assumed that the beam has a constant axial velocity and is subject to uniform axial tension. The analysis is based on higher-order theories that have been presented by Carrera Unified Formulation (CUF). In the CUF technique, the three dimensional (3D) displacement fields are expressed as the approximation of the arbitrary order of the displacement unknowns over the cross-section. This higher-order expansion is considered in equivalent single layer (ESL) model. The governing equations of motion are obtained via Hamilton\' s principle. Finally, several numerical examples are presented and the effect of the ply-angle, travelling speed and axial tension on the natural frequencies and beam stability are demonstrated.

This article is devoted to the evaluation of refined theories for static response analysis of piezoelectric plate. The Carrera Unified Formulation (CUF) is employed to generate the refined plate models. The CUF allows the hierarchical implementation of refined models based on any-order expressions of the unknown variables. Equivalent single layer (ESL) and layerwise (LW) approaches are used to generate the refined models. The governing equations are obtained considering Navier-type, closed-form solutions. The axiomatic/asymptotic technique is employed in order to evaluate the relevance of each model term. This technique computes the relevance of a model term by measuring the error introduced with its deactivation with respect to a reference solution. The axiomatic/asymptotic technique is applied considering the sensor and actuator configurations for piezoelectric plates. Moreover, the analyses are performed taking into account the influence of the length-to-thickness ratio (a/h) and the use of isotropic or orthotropic materials. “Best” models are proposed and the stress/displacement components and electric potential distributions are evaluated by means of these reduced models.

Local FEM Analysis of Composite Beams and Plates: Free-Edge effect and Incompatible Kinematics Coupling

Advanced and refined variable-kinematics plate theories built with a hierarchical approach in an extended framework of Carrera's unified formulation (CUF) are combined with Ritz and Galerkin methods to deal with a thermo-mechanical buckling analysis of anisotropic multilayered composite and sandwich plates. Buckling interaction curves and stability envelopes for different thermal and mechanical loading combinations are presented. The influence of the kinematics description and the expansion orders upon the results accuracy is evaluated. The effect of the transverse normal deformation on critical temperature parameters is thoroughly investigated. Convergence and results accuracy are discussed.

In intelligent coal mining systems, the primary structural component often comprises a sandwich plate, valued for its high strength, wear resistance, and lightweight properties. This component is vital for maintaining equipment performance in demanding subterranean environments. This research proposes a robust mathematical framework based on the Carrera Unified Formulation (CUF) and the principle of virtual displacements (PVD) to model and optimize the electromechanical behavior of piezoelectric shunt damping systems for subsonic flutter suppression and energy harvesting. Utilizing CUF’s high-order modeling precision, the framework captures the complex aeroelastic and electroelastic couplings under subsonic flow conditions with high fidelity. A multimodal shunt circuit design is developed and optimized to maximize both vibration energy dissipation and electrical energy harvesting, thereby enhancing system stability and extending operational lifespan. The effects of circuit tuning, structural parameters, and external aerodynamic excitations on flutter mitigation and power output are systematically investigated. Comparative numerical results show that CUF-based models offer greater predictive accuracy for multimodal dynamics and superior optimization capabilities relative to traditional finite element methods. This study advances the integration of structural mechanics, electromechanical interactions, and energy harvesting technologies, promoting the development of self-powered, vibration-controlled, and durable mining equipment. The approach supports next-generation energy-efficient mining solutions through rigorous modeling of variable expansions along thickness directions via equivalent single-layer (ESL) and layer-wise (LW) descriptions.

Assessment of the apparent bending stiffness and damping of multilayer plates; modelling and experiment